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‘Whenever you encounter a system that seems so irrational, you should ponder what's going on beneath the surface.’

‘Man is an irrational being, morals are irrational, and have no metaphysical foundation which make them "real" or worth paying any attention to.’

2Mathematics (of a number, quantity, or expression) not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal. Examples of irrational numbers are the number π and the square root of 2.

‘The square root of 2 is an irrational number because it can't be written as a ratio of two integers.’

‘A transcendental number is an irrational number that is not a root of any polynomial equation with integer coefficients.’

‘How can mathematical concepts like points, infinitesimally small quantities, or irrational numbers be anything but products of our minds?’

‘He considered computation with irrational numbers and polynomials to be part of algebra.’

‘What about a seed angle derived from the golden ratio, an irrational number?’

noun

Mathematics

An irrational number.

‘Any finite segment can be continued to produce a rational and any finite segment can be continued to produce an irrational.’

‘His commentary to Euclid is of interest because of its discussion of unordered irrationals.’

‘Whether such quirks in the irregularity of irrationals have any implications for number theory remains an open question for mathematicians.’

‘If we chop off an infinite cfe after a finite number of steps then we will create a rational approximation to the original irrational.’

‘Eudoxus's definition of equal ratios corresponds exactly to the modern theory of irrationals.’

Origin

Late Middle English: from Latin irrationalis, from in- not + rationalis (see rational).